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Appendix II.                              841

P. 4.00. Thick Cylinders.It appears from Lamp's formula
(p. 399) that in an originally unstrained cylinder, if the pressure
from inside be greater than f the tensile strength of the material,
no amount of thickness can prevent bursting. This difficulty can
be to some extent overcome by the principle of initial stressing,
p. 758. It has also been found that if the fluid pressure in cast-
iron cylinders be gradually increased beyond the calculated limit,
the internal diameter may be permanently stretched, and then /
has been known to reach 3 tons sq. in. with safety.

The formulae used in designing built-up guns, deduced from
Lame', is here given (see also Fig. 749).

/0 = internal pressure on firing

/x = pressure between A and B tubes on firing

/2 = pressure between B and c tubes on firing.

/0 = maximum hoop tension in cylinder A
^ = maximum hoop tension in cylinder B
/2 = maximum hoop tension in cylinder c.

r0  internal radius of cylinder A
r-L = internal radius of cylinder B
r^ = internal radius of cylinder c
r% = external radius of cylinder c.

Then>    A - ~S> Co + A) +A          A =   aTa

""

To obtain these results, each outer tube must be smaller than
the next inner tube by an amount called shrinkage.

Q _ /Shrinkage between ) _ A ~A + 4 - *0
^2 ~ \         A and B         f ~         E~   " "      x

Shrinkage between I _     /2+A-(/0-A)

B and. c

I _
)

_T__«,^
E

The formula for / may be extended to four or reduced to two